#https://datatables.net/reference/option/
options(DT.options = list(scrollX = TRUE, pagin=TRUE, fixedHeader = TRUE, searchHighlight = TRUE))

Intro

Check out this Kaggle webpage

In one piped statement:

  1. read in data
  2. convert char to factor vars
  3. rename all colnames lowercase
  4. order cols by name: alphabetically
  5. order cols by datatype: nominal, then numeric

Get Data

a = read_csv(here::here('/Clustering/Mall_Customers.csv')) %>%  #1
  mutate(across(where(is.character),as.factor)) %>% #2
  clean_names(.) %>% #3
  select(sort(tidyselect::peek_vars())) %>% #4
  select(where(is.factor), where(is.numeric)) %>%  #5
  select(-customer_id)

#Split Data

set.seed(321)
split = a %>% initial_split()
train = split %>% training()
test = split %>% testing()

EDA: nom vars

check head rows

train %>% select(where(is.factor)) %>% head %>% DT::datatable()

glimpse structure

train %>% select(where(is.factor)) %>% glimpse
Rows: 150
Columns: 1
$ gender <fct> Male, Male, Female, Female, Female, Female, Female, Male, Female, Male, Female, Female...

check for missing values

train %>% select(where(is.factor)) %>% miss_var_summary()

distribution: counts of unique levels

sapply(train %>% select(where(is.factor)), n_unique)
gender 
     2 

reference: names of unique levels

sapply(train %>% select(where(is.factor)), unique)
     gender  
[1,] "Male"  
[2,] "Female"

binarize gender to numeric var

train = train %>% mutate(gender = if_else(gender == 'Male', 1, 0))

distribution: viz

ggplotly(
train %>% count(gender = factor(gender)) %>%
  mutate(percent = n/nrow(train)) %>%
  ggplot(aes(percent, gender, fill = gender)) +
  geom_col() +
  scale_x_continuous(labels = scales::percent) +
  labs(x = '', y = '', title ='Gender Percent Breakdown: 1 = Male, 0 = Female') +
  theme(legend.position = 'none')
)

EDA: num vars

check head rows

train %>% select(where(is.numeric)) %>% head %>% DT::datatable()

glimpse structure

train %>% select(where(is.numeric)) %>% glimpse
Rows: 150
Columns: 4
$ gender               <dbl> 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, ...
$ age                  <dbl> 19, 21, 20, 31, 22, 35, 23, 64, 30, 67, 35, 24, 37, 22, 52, 35, 35, 25, ...
$ annual_income_k      <dbl> 15, 15, 16, 17, 17, 18, 18, 19, 19, 19, 19, 20, 20, 20, 23, 23, 24, 24, ...
$ spending_score_1_100 <dbl> 39, 81, 6, 40, 76, 6, 94, 3, 72, 14, 99, 77, 13, 79, 29, 98, 35, 73, 73,...

check for missing values

miss_var_summary(train %>% select(where(is.numeric)))
NA

distribution: viz

There appears to be outliers for male annual income

distribution: viz

distribution: viz

pairwise correlations: viz

GGally::ggcorr(train %>% select(where(is.numeric)), low = '#990000', mid = '#E0E0E0', high = '#009900', label = TRUE)

Preprocessing

Reference: (package recipes)[https://recipes.tidymodels.org/reference/index.html]

normalize data

Create matrix

Determine Optimal Number of Clusters

Documentation

1) silhouette analysis with kmeans and euclidean distancing

factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "euclidean"),
  FUNcluster=kmeans,
  method="silhouette"
  ) +
  theme_classic()

2) silhouette analysis with kmeans and manhattan distancing

factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "manhattan"),
  FUNcluster=cluster::pam,
  method="silhouette"
  ) +
  theme_classic()

3) silhouette analysis with pam and euclidean distancing

factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "euclidean"),
  FUNcluster=kmeans,
  method="silhouette"
  ) +
  theme_classic()

4) silhouette analysis with pam and manhattan distancing

factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "manhattan"),
  FUNcluster=cluster::pam,
  method="silhouette"
  ) +
  theme_classic()

Finalize Models with Optimal Number of Clusters and Distancing Method

Kmeans

km = eclust(
  train.matrix,
  FUNcluster="kmeans",
  k=9,
  hc_metric = "manhattan"
  )

PAM

pam = eclust(
  train.matrix,
  FUNcluster="pam",
  k=9,
  hc_metric = "manhattan"
  )

train %>%
  mutate(gender = factor(if_else(gender == 1, 'Male', 'Female'))) %>%
  group_by(cluster, gender) %>%
  summarise(
    mean.age = mean(age, na.rm = TRUE),
    mean.income = mean(annual_income_k, na.rm = TRUE),
    mean.spending.score = mean(spending_score_1_100, na.rm = TRUE)
  )
`summarise()` regrouping output by 'cluster' (override with `.groups` argument)
xvars = train %>% select(-cluster) %>% names %>% as.character()

jpal = colorRampPalette(RColorBrewer::brewer.pal(8,'Dark2'))(25)

train %>% plot_ly(y = ~cluster, x = ~eval(as.name(xvars[2])), color = ~cluster, colors = jpal) %>% add_boxplot() %>% hide_legend() %>% layout(
  title = paste0(xvars[2],' by cluster'), xaxis = list(title = xvars[2]))


train %>% plot_ly(y = ~cluster, x = ~eval(as.name(xvars[3])), color = ~cluster, colors = jpal) %>% add_boxplot() %>% hide_legend() %>% layout(
  title = paste0(xvars[3],' by cluster'), xaxis = list(title = xvars[3]))


train %>% plot_ly(y = ~cluster, x = ~eval(as.name(xvars[4])), color = ~cluster, colors = jpal) %>% add_boxplot() %>% hide_legend() %>% layout(
  title = paste0(xvars[4],' by cluster'), xaxis = list(title = xvars[4]))

Notes

  1. Try Other Popular Clustering Methods
    • hierarchical clustering
    • dbscan
---
title: "Clustering Mall Customers"
author: "Jeremiah W"
date: 'October 28 2020'
output:
  html_document:
    toc: yes
    toc_depth: '2'
    df_print: paged
  html_notebook:
    theme: paper
    code_folding: hide
    df_print: hide
    toc: yes
    toc_depth: 2
    toc_float:
      collpased: no
      smooth_scroll: no
---

```{r}
#https://datatables.net/reference/option/
options(DT.options = list(scrollX = TRUE, pagin=TRUE, fixedHeader = TRUE, searchHighlight = TRUE))
```

```{r include=FALSE}
library(DataExplorer);library(data.table);
library(extrafont);library(formattable);library(GGally);library(here);
library(janitor);library(lubridate);library(naniar);
library(patchwork);library(PerformanceAnalytics);
library(plotly);library(RColorBrewer);library(readxl);
library(skimr);library(tidyverse);library(scales)

library(caret);library(tidymodels);library(h2o)

library(kmed);library(NbClust);library(factoextra)
```

# Intro
Check out [this Kaggle webpage](https://www.kaggle.com/vjchoudhary7/customer-segmentation-tutorial-in-python)

In one piped statement:
  
1. read in data
2. convert char to factor vars
3. rename all colnames lowercase
4. order cols by name: alphabetically
5. order cols by datatype: nominal, then numeric

# Get Data
```{r message=FALSE}
a = read_csv(here::here('/Clustering/Mall_Customers.csv')) %>%  #1
  mutate(across(where(is.character),as.factor)) %>% #2
  clean_names(.) %>% #3
  select(sort(tidyselect::peek_vars())) %>% #4
  select(where(is.factor), where(is.numeric)) %>%  #5
  select(-customer_id)
```

#Split Data
```{r}
set.seed(321)
split = a %>% initial_split()
train = split %>% training()
test = split %>% testing()
```

# EDA: nom vars

### check head rows
```{r}
train %>% select(where(is.factor)) %>% head %>% DT::datatable()
```
### glimpse structure
```{r}
train %>% select(where(is.factor)) %>% glimpse
```

### check for missing values
```{r}
train %>% select(where(is.factor)) %>% miss_var_summary()
```
### distribution: counts of unique levels
```{r}
sapply(train %>% select(where(is.factor)), n_unique)
```

### reference: names of unique levels
```{r}
sapply(train %>% select(where(is.factor)), unique)
```
### binarize gender to numeric var
```{r}
train = train %>% mutate(gender = if_else(gender == 'Male', 1, 0))
```


### distribution: viz
```{r cache=TRUE}
ggplotly(
train %>% count(gender = factor(gender)) %>%
  mutate(percent = n/nrow(train)) %>%
  ggplot(aes(percent, gender, fill = gender)) +
  geom_col() +
  scale_x_continuous(labels = scales::percent) +
  labs(x = '', y = '', title ='Gender Percent Breakdown: 1 = Male, 0 = Female') +
  theme(legend.position = 'none')
)
```

# EDA: num vars

### check head rows
```{r}
train %>% select(where(is.numeric)) %>% head %>% DT::datatable()
```

### glimpse structure
```{r}
train %>% select(where(is.numeric)) %>% glimpse
```

### check for missing values
```{r  rows.print = 10}
miss_var_summary(train %>% select(where(is.numeric)))

```

### distribution: viz
```{r cache=TRUE}
DataExplorer::plot_boxplot(train %>% select(where(is.numeric), gender), by = 'gender')
```

<h3 style="color: red; font-size:14px;">There appears to be outliers for male annual income</h2>

### distribution: viz
```{r cache=TRUE}
DataExplorer::plot_histogram(train %>% select(where(is.numeric)))
```

### distribution: viz
```{r cache=TRUE}
DataExplorer::plot_density(train %>% select(where(is.numeric)))
```

### pairwise correlations: viz
```{r cache=TRUE}
GGally::ggcorr(train %>% select(where(is.numeric)), low = '#990000', mid = '#E0E0E0', high = '#009900', label = TRUE)
```

# Preprocessing
Reference: (package recipes)[https://recipes.tidymodels.org/reference/index.html]

### normalize data
```{r}
### normalize data so certain features aren't unfairly weighted
recipe = train %>% recipe() %>% step_normalize(all_numeric())

train.normalized = recipe %>% prep() %>% juice
```
## Create matrix
```{r cache=TRUE, echo=FALSE}
train.matrix = train.normalized %>% as.matrix()
```

# Determine Optimal Number of Clusters

[Documentation](https://rstudio-pubs-static.s3.amazonaws.com/455393_f20bacf1329a49dab40eb393308b33eb.html#choosing-optimal-number-of-clusters)

### 1) silhouette analysis with kmeans and euclidean distancing
```{r}
factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "euclidean"),
  FUNcluster=kmeans,
  method="silhouette"
  ) +
  theme_classic()
```

### 2) silhouette analysis with kmeans and manhattan distancing
```{r}
factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "manhattan"),
  FUNcluster=cluster::pam,
  method="silhouette"
  ) +
  theme_classic()
```

### 3) silhouette analysis with pam and euclidean distancing
```{r}
factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "euclidean"),
  FUNcluster=kmeans,
  method="silhouette"
  ) +
  theme_classic()
```

### 4) silhouette analysis with pam and manhattan distancing
```{r}
factoextra::fviz_nbclust(
  train.matrix,
  diss = dist(train.matrix, method = "manhattan"),
  FUNcluster=cluster::pam,
  method="silhouette"
  ) +
  theme_classic()
```

# Finalize Models with Optimal Number of Clusters and Distancing Method

## Kmeans
```{r}
km = eclust(
  train.matrix,
  FUNcluster="kmeans",
  k=9,
  hc_metric = "manhattan"
  )
```

## PAM
```{r}
pam = eclust(
  train.matrix,
  FUNcluster="pam",
  k=9,
  hc_metric = "manhattan"
  )
```


```{r}
train = train %>% mutate(cluster = factor(pam$cluster, levels = 1:9))

train %>%
  mutate(gender = factor(if_else(gender == 1, 'Male', 'Female'))) %>%
  group_by(cluster, gender) %>%
  summarise(
    mean.age = mean(age, na.rm = TRUE),
    mean.income = mean(annual_income_k, na.rm = TRUE),
    mean.spending.score = mean(spending_score_1_100, na.rm = TRUE)
  )
```
```{r}
glimpse(train)
train %>% count(cluster) %>% arrange(-n)
```
```{r}
ggplotly(train %>% mutate(gender = factor(if_else(gender == 1, 'Male', 'Female'))) %>% ggplot(aes(cluster, annual_income_k, fill = cluster)) + geom_boxplot() + facet_wrap(~gender) +
           scale_y_continuous(breaks = seq(
             min(train$annual_income_k),
             max(train$annual_income_k), 10
             )))

ggplotly(train %>% mutate(gender = factor(if_else(gender == 1, 'Male', 'Female'))) %>% ggplot(aes(cluster, age, fill = cluster)) + geom_boxplot() + facet_wrap(~gender))

ggplotly(train %>% mutate(gender = factor(if_else(gender == 1, 'Male', 'Female'))) %>% ggplot(aes(cluster, spending_score_1_100, fill = cluster)) + geom_boxplot() + facet_wrap(~gender))

```

```{r}
xvars = train %>% select(-cluster) %>% names %>% as.character()

jpal = colorRampPalette(RColorBrewer::brewer.pal(8,'Dark2'))(25)

train %>% plot_ly(y = ~cluster, x = ~eval(as.name(xvars[2])), color = ~cluster, colors = jpal) %>% add_boxplot() %>% hide_legend() %>% layout(
  title = paste0(xvars[2],' by cluster'), xaxis = list(title = xvars[2]))

train %>% plot_ly(y = ~cluster, x = ~eval(as.name(xvars[3])), color = ~cluster, colors = jpal) %>% add_boxplot() %>% hide_legend() %>% layout(
  title = paste0(xvars[3],' by cluster'), xaxis = list(title = xvars[3]))

train %>% plot_ly(y = ~cluster, x = ~eval(as.name(xvars[4])), color = ~cluster, colors = jpal) %>% add_boxplot() %>% hide_legend() %>% layout(
  title = paste0(xvars[4],' by cluster'), xaxis = list(title = xvars[4]))
```

```{r}

```


# Notes

1. Try Other Popular Clustering Methods
    + hierarchical clustering
    + dbscan